The Legendre transform is an important tool in theoretical physics，and the Legendre transform of multivariable function has manifestly symmetry. Ensemble is the core content of statistical mechanics. Using the dimensionless of Legendre transform，the Legendre transform of partition function can be analogy definition from the Legendre transform of entropy，which is characteristic function of microcanonical ensemble. Meanwhile，the characteristic function， partition function of every ensemble and their relations as well as the relevant thermodynamics formula，can be obtained.